AFISI, OSENI TAIWODEPARTMENT OF PHILOSOPHY,LAGOS STATE UNIVERSITY, OJO, LAGOS, NIGERIA.EMAIL:afisitaiwo@yahoo.com

THE PROBLEM OF INDUCTION AND KARL POPPER’S HYPOTHETICO-DEDUCTIVE METHODOLOGY: A CRITICAL EVALUATION

ABSTRACTThe focus of this paper is to examine the problem of induction as a methodology for science. It also evaluates Karl Popper’s deductive approach as the suitable methodology for scientific research. Popper calls his theory ‘hypothetico-deductive methodology’. However, this paper argues the thesis that Popper’s theory of hypothetico-deductive methodology, which he claims is the only appropriate methodology of science is fraught with some theoretical difficulties, which makes it unacceptable. Popper’s logical asymmetry between verification and falsification, we argue, is philosophically untenable. We argue the thesis for the complementarity of both inductive and deductive methodology in scientific investigation. This study seeks to establish the resonance of accepting both deductive and inductive reasoning as the basic methodologies upon which scientific research and discoveries proceed.

INTRODUCTION

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The most appropriate methodology suitable for scientific investigation

and research has been an issue of controversy among scholars,

scientists and as well as philosophers of science. Ideologically, scholars

are divided on the most appropriate methodology for determining

empirical truth. Broadly categorized, the critical divide has been

between inductive and deductive methodologies.

Recent trends in philosophy of science discourse revolve around the

problem of methodology of scientific inquiry, the factors that could

enhance the advancement of science, the question of truth and

certainty as well as the issue of rationality of scientific discoveries.

More fundamental in this discourse is the methodological problem of

scientific research. In fact, a number of ideologies have emerged in

response to the challenges posed by the issue of methodology of

science.

The relativists, for instance, see scientific truth in terms of a period of

reference, environment and orientation. To the realist, a statement in

science is either true or false; there is no mid-way between the two.

The instrumentalists are rather interested in the function that theories

play in science. They see theories as necessary instruments in science,

which essentially, are meant to make prediction with precision possible

and to offer explanation of events in nature.

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Incidentally, Francis Bacon, Isaac Newton, and others considered D the

basis of scientific method. By this inductive approach to scientific

method, one makes a series of observations and forms a universal

generalization. If correct and stated in a sufficiently accurate way, an

inductively arrived-at statement relieves others of the need for making

so many observations and allows them to instead use the

generalization to predict what will happen in specific circumstances in

the future.

The logical positivists, on their own, are interested both in the

methodology of science as well as the relationship between science

and metaphysics. They also thought highly of the principle of inductive

procedure as a basis for scientific knowledge. They, however, use their

principles of verifiability and confirmabilty to dismiss the propositions

of metaphysics as nonsensical, and as having no bearing in the

acquisition of knowledge.

Following the logical positivists, David Hume launched an attack on

metaphysics which he saw as pure sophistry and illusion. But Hume

criticized induction and argued against it as the best model or method

of science. Karl Popper also condemned the inductive model of

science and introduced the deductive method which he termed the

‘hypothetico-deductive method of science.

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THE PROBLEM OF INDUCTION

The term induction is a process or method of reasoning in which the

premises of an argument are believed to support the conclusion. It is

the method of inferring general theories or laws from particular

instances that have been observed. According to Kemeny, (1959, 93)

induction is the “process by which the scientist forms theory to explain

the observed facts, it is a reasoning drawn from the past to the future

in the expectation that the future will continue to behave in the same

manner as in the past”. What this simply implies is that the fact that

the sun rises every morning to the best of our knowledge in the past

gives us the cause to believe that it will rise in such a way in the

future.

It is pertinent to mention that induction presupposes certain basic

assumptions:

1. that there is a necessary connection between one event and another, that is, between a cause and its effect.

2. that nature is uniform and behaves the same way anywhere and at all times.

3. that the future will be like the past, and that what happened in the past will also happen in the future.

4. that what we have observed to be the case in many instances will be the case in all instances.

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Aristotle was first to establish the mental process of inductive-

deductive method as a class of reasoning. He views scientific inquiry as

a progression from observation to generalizations and back to

observations. To Aristotle, explanatory principles sould be induced

from observations. Robert Grosseteste and Roger Bacon both affirm

Aristotle’s inductive-deductive model of scientific method.

Crombie(1953: 52) notes that Grosseteste refers to the inductive stage

as a ‘resolution’ of phenomena into constituent elements, and to the

deductive stage as a ‘composition’ in which these elements are

combined to reconstruct the original phenomena. Losee (1993: 32)

also mentions that Grosseteste method of induction specifies an

inductive assent from statements about phenomena to elements from

which the phenomena may be reconstructed. In his book, The Opus

Majus, Roger Bacon (1962: 615) also emphasizes that successful

application of this inductive procedure depends on accurate and

extensive factual knowledge. To him, the factual base of a science

often may be augmented by active experimentation.

In a similar vein, Francis Bacon, regarded as the champion of the

inductive-experimental method, also advocates for the inductive

process for scientific investigations. Like, Aristotle, Bacon sees science

as a progression from observations to general principles and back to

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observations. However, Bacon criticizes Aristotle’s on the basis that

Aristotle’s induction relies on simple enumeration; and secondly that

Aristotle reduced science to deductive logic by overemphasizing the

deduction of consequences from first principles. To Bacon, deductive

arguments are of scientific value only if their premises have proper

inductive support. (Losee 1993, 67).

John Stuart Mill also systematized the inductive methods with his

formulation of the five canons of induction. Theses include the method

of agreement; the method of difference; the joint method of agreement

and difference; the method of residues; and the method of

concomitant variation. (Copi and Cohen 2006, 455) To Mill, these

procedures are means of testing scientific hypotheses. They are the

tools with which causal relations may be discovered, and canons with

which causal connections may be proved. However, Copi and Cohen

(2006) mention “that Mill was wrong on both counts…….. That the

methods are indeed of the very greatest importance, their role in

science is not so majestic as he supposed.”

Jevon (1958) also criticizes Mill’s claim that the justification of

hypotheses is of inductive schemata. Jevon emphasizes that in order

to show that a hypotheses has consequences that agree with what is

observed is to utilize deductive arguments.

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In a similar vein, David Hume denies the logical admissibility of

inductive reasoning by criticizing the theory of causality. In his Enquiry

Concerning Human Understanding, Hume articulated his view that the

inductive inference operates on the principle that the past acts as a

reliable guide to the future (this is sometimes called the principle of

the uniformity of nature).

Although Hume did not use the word induction, but his critical analysis

of the principle of causality was in fact a critical analysis of his

inductive method.(Omoregbe 1996, 118). For Hume, “every event,

whether cause or effect, is utterly distinct and a separate entity. In a

word, every effect is a distinct event from its cause” (Hume 1955,

118).

Hume thus concludes that our inductive practices have no rational

foundation, for no form of reason will certify it. To Hume, the assumed

necessary connection between a cause and an effect derives from our

habit of associating together two things that we have repeatedly seen

occurring together in the past. Thus, it is an assumption that there is a

necessary connection between them, that the first causes the second.

POPPER’S ARGUMENT AGAINST INDUCTION

Popper’s contribution to philosophy of science is his attempt to deal

with the philosophical problem of induction. Karl popper disputes the

existence, necessity and validity of any inductive reasoning. He agrees

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with Hume that there is a no necessary connection between a cause

and an effect, and that we can never draw a logically valid conclusion

from some observed cases to all cases. Popper accepts Hume's

conclusion that inductive inference is not rationally justifiable. He thus,

rejects the principles of induction as “superfluous, and that it must

lead to logical inconsistencies”(Popper 1977, 29). The principle, he

argues, can lead to infinite regress. Nevertheless, Popper disagrees

with Hume’s observation that the assumed necessary connection

derives from our habit of seeing two things together in the past. If

induction originates from habit, where does habit itself originate from?

But while Hume says habit originates from repetition, Popper disagrees

and contends that habit is prior to repetition. To popper, habit is

already formed before repetition begins. Thus, repetition cannot be the

source of habit. Popper contends that habit arises from expectation,

prior to repetition. He points out that we naturally expect regularity

and uniformity from nature even before we begin to experience

repetition. Thus, induction is not based on habit as Hume would have

us believe, but on expectation which is then followed by observation.

This expectation is already a theory, which means that theory comes

before observation, and not the other way round.

ON FALSIFICATION AND CORROBORATION

Popper contends that theories are prior to observation, and they are

derived from expectations. Theories are conjectures put forward to be

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tested by observation, to be falsified or corroborated by observation.

Popper explains that a theory can never be confirmed by observation,

it can only be corroborated, while the possibility of it been falsified in

future remains open. If a theory fails to yield the expected result or if

experience negates a theory, and it is falsified then it should be

abandoned.

Theories that have not yet been falsified, or those that have been

repeatedly corroborated by experience can still be falsified by future

experience and observation. Science, according to Popper proceeds by

the method of conjectures and refutations, by trial and error. It is not

founded on any solid rock. To Popper “the empirical basis of objective

science has nothing absolute about it. Science does not rest upon solid

‘bedrock’; on the contrary, it is like a building erected on piles”.

(Popper 1959, 11). Popper also contends that “the belief in scientific

certainty and in the authority of science is just wishful thinking.

Science is fallible because science is human.” (Popper 1945, 375).

Popper admits that modern science has made tremendous progress.

To Popper, this progress is not due to the method of induction. He

argues that science does not employ the inductive method. Instead,

science proceeds by the method of conjectures and refutations, trial

and error. Thus, repeated observations and experiments function in

science as tests of our conjectures or hypotheses, i.e., as attempted

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refutations.(Popper 1963, 55). To Popper, a scientific theory is by its

nature falsifiable. The more falsifiable a theory is, the more scientific it

becomes.

KARL POPPER’S HYPOTHETICO-DEDUCTIVE METHODOLOGY

Popper rejects the traditional inductive model in science and replaces

it with his own methodology, the ‘hypothetico-deductive methodology’.

Popper here reiterates that the methodology actually employed by

scientists is not the inductive method but the hypothetico-deductive

method.

Popper rejects the traditional inductive model and says that it is not

the actual methodology of science. He replaces with what he claims to

be the methodology actually used by science. According to Popper, the

hypothetico-deductive method begins with a problem, followed by a

theory as a tentative explanation or solution to the problem,

experimentation or observation is then carried out with a view to

falsifying the theory. The theory could then be falsified, refuted and

then rejected, or it could be ‘corroborated’ by repeated experiment, in

which cases it is accepted and used continuously. Popper insists that

observation does not come before theory as it is believe in the

traditional inductive methodology. On the contrary, theory comes

before observation.(Popper 1963, 46). So, according to Popper, that

one can start with pure observation alone without anything in the

nature of a theory is meaningless and nonsensical.

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In Popper’s methodology, only theoretical systems capable of being

refuted by tests are scientific. Such systems are falsifiable by

systematic experimentation. Therefore, for Popper, falsifiability and

testability mean the same thing, since every genuine test of a theory is

an attempt to falsify it. Logically, the characterisation of such falsifiable

or testable systems involves the attempt to spell out the logical

relations holding between a theory and the class of what Popper called

‘basic statements’. (Popper 1959, 100).

A scientific theory is taken to be falsified if there are accepted basic

statements which clash with it. Popper argues that if accepted basic

statements contradict a theory, then they provide adequate grounds

for its falsification only if they corroborate a falsifying hypothesis

simultaneously. Thus, the experimental situation in which the scientist

finds himself more often than not involves crucial experiments

designed to decide between two hypotheses. In so far as these

hypotheses differ in some way, the experiment has to corroborate one

or the other, and such corroboration is effected when the competing

hypotheses are confronted with accepted basic statements. (Anele

1997, 25)

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One of Popper’s arguments against the theory of induction is his

elaboration of the idea of corroboration. A theory is said to be

corroborated so long as it does not contradict the accepted basic

statements. To Popper, corroboration means confirmation in the

process of testing scientific hypotheses. However, much corroboration

is found if a hypotheses is still not conclusively proved true.(Flew

1979, 73). Popper compares two theories in order to find which one

has lesser or greater verisimilitude. Popper explains that when two

theories for example are corroborated, the theory, which passes lots of

tests, is likely to have greater verisimilitude. This implies that the

theory, which has greater verisimilitude, has more truth and less

falsehood. (Afisi 2003, 104). Popper maintains that a hypothesis which

is falsifiable in a higher degree, or the simpler hypotheses, is also the

hypothesis which is corroborated to a higher degree. If we have

hypotheses A and B as competing theories at a point in time, and we

know that B has survived severer tests than A, then B has greater

verisimilitude i.e. more truth and less falsehood at that point in time.

(Anele 1997, 26)

Although, Popper is aware that the comparison of two statements or

theories in terms of their degrees of corroboration is problematic. He

says we can only speak roughly in terms of positive degrees of

corroboration, negative degrees of corroboration, and the like.(Popper

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1959, 268). This may render corroboration otiose in the logic of

science. But Popper’s strategy for preventing that is the articulation of

some methodological rules; for instance the rule that a falsified theory

should not receive a positive corroboration appraisal.

It is pertinent to pause at this juncture in order to know whether

Popper intends to use his idea of inventing theories of higher degrees

of corroboration to be used in place of the idea of truth as the aim of

science. This is because Popper had variously described the objective

of scientific research programmes as “discovery of truth”, “explanation

of reality”, “invention of theories of greater verisimilitude” among

others. But in the The Logic of Scientific Discovery, he was very

skeptical in the use of ‘truth’ to characterize scientific theories.(Kraft

2004, 112). For Popper, the falsificationist methodology does not need

the concepts of ‘true’ and ‘false’.

Although, the concepts of true and false are regular logical concepts

among scientists. Both concepts are timeless in the sense that when a

statement is true or false, it is true or false forever. This explains the

situation when, for instance, a theory which is taken to be true

yesterday is now stated to be false today, in the light of new

knowledge. What this simply implies is that the theory was true

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yesterday but became false today because a new discovered

knowledge has made it false.

However, the concept of corroboration is essentially different from this.

We appraise a statement as corroborated with respect to some system

of basic statements, a system accepted up to a particular point in time.

In the words of popper:

The corroboration which a theory has received up to yesterday is logically not identical with the corroboration which a theory has received up to today. Thus we must attach a subscript, as it were, to every appraisal of corroboration- a subscript charaterising the system of basic statements to which the corroboration relates(for example, by the date of its acceptance). (Popper 1959, 275)

It is clear from the foregoing that Popper’s idea of corroboration of

scientific theories is not the same with the concepts of truth and

falsehood of scientific theories usually held by other scientists. This is

because the concepts of true and false are free from temporal

considerations, in their objective senses. But one and the same

theories may have different corroboration values all of which can

actually be true at the same time.

EVALUATION AND CONCLUSION

Going by Popper’s criticism of the inductive model of science one

would appreciate his position upon the basis that deductive arguments

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are usually always rationally and logically true. In deductive logic, for

instance:

All human beings are mortalSocrates is a human being Therefore, Socrates is mortal

The conclusion of this argument is derived logically from the premises.

This argument is naturally, rationally, logically and necessarily true.

This is as against the example of inductive argument in logic.

One essential feature of inductive argument is that there is always a

‘gap’ or an inductive leap from the premises to the conclusion of an

argument. The conclusion of an inductive argument can only follow

from the premises with some degree of probability. For instance:

Cows are mammals and feed their young with milkSheep are mammals and feed their young with milkDogs are mammals and feed their young with milkTherefore, all mammals and feed their young with milk

Nevertheless, we cannot categorically affirm that Popper’s

hypothetico-deductive methodology successfully solved the problem of

induction in science. Popper’s logical asymmetry between verification

and falsification, we argue, is fraught with technical errors. The

inconsistency in this analysis is that Popper condemns induction with

the right hand and embraces it with the left. This asymmetry between

verifiability and falsifiability result only from the logical form of

universal statements but Popper admits that they can also be

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contradicted by singular statements with the help of modus tollens of

classical logic. To Popper, such an argument to the falsity of universal

statements is the only strictly deductive kind of inference that

proceeds, as it were, in the ‘inductive direction’; that is, from singular

to universal statements. (Popper 1977, 41). This, we say, is antithetical

to Popper’s absolute rejection of the inductive method

Again, there is no denying the fact that every philosophical enterprise

has a metaphysical basis. The inductive model of science is, in fact, a

priori. The inductive reasoning constitutes the metaphysical foundation

of modern science. The inductive model is supra-empirical in which no

empirical investigation or experiment can establish. It is a probability

based model of enquiry. Thus, we cannot rule out the traces of

inductive processes in empirical science. Contrary to the contention of

Hume and Popper, science actually employs the inductive method

which is implied even in Popper’s own hypothetico-deductive method.

Popper’s admittance of the importance of metaphysics to empirical

science relates to his embrace of induction. In his words:

I do not even go so far as to assert that metaphysics has no value for empirical science. for it cannot be denied that along with metaphysical ideas which have obstructed the advance of science there have been others-such as speculative atomism-which have aided it. And looking at the matter from the psycholological angle, I am inclined to think that scientific discovery is impossible without faith in ideas which are of a purely speculative kind, and sometimes even quite hazy; a faith which is completely unwarranted from the

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point of view of science, and which, to that extent, is ‘metaphysical’.

It is clear from the above that induction is implied in Popper’s own

hypothetico-deductive method. Even Popper’s falsifiability and

corroboration theses are arrived at inductively. It is therefore on this

basis that we argue the thesis for the complementarity of both

inductive and deductive methodology in scientific investigation. This is

because it is this induction that enables scientists to predict the

outcome of a scientific test. No doubt, prediction is one of the basic

features of science. Prediction, which is embedded in probability, is

essentially, one of the methods of induction. We can therefore

conclude that inductive method cannot be totally abandoned in

science. We therefore reiterate that both deductive and inductive

reasoning are the basic methodologies upon which scientific research

and discoveries proceed.

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Crombie A.C. (1953), Robert Grosseteste and the Origins of Experimental Science

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Flew Anthony (1979), A Dictionary of Philosophy, London: Pan Books

Hume David (1955), Enquiry Concerning Human Understanding, Indianapolis: Bobbs Inc.

Kraft Victor (2004), “Popper and the Vienna Circle” in Paul A. Shilpp, The Philosophy of Karl Popper, Illinois: Open Court

Kemeny Joseph (1959), A Philosopher’s Look at science, Princeton: Nostrand

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